(a) Find all nonsymmetric 2x2 matrices A such that AA^T =(A^T)A

(b) Let S(subscript1) be the set of all matrices found in part (a) and let S(subscript2) be the set of all 2x2 scalar matrices. Define W = S(subscript1) U S(subscript2)

(i) Show that W is a subspace of M(subscript2x2)

(ii) Find dim (W)

I'm really struggling in this class so i have no clue how to do this. Help?